Application of Jensen's inequality to adaptive suboptimal design

In this paper, it is shown that, if the expected cost-to-go functions generated by a suboptimal design for a partially observed, discrete-time, Markov decision problem with a specific state measurement quality are concave, then the suboptimal design has a desirable adaptivity characteristic relative to that state measurement quality. Optimal strategies are shown to possess this adaptivity characteristic, as does a suboptimal design presented in an example.This research was supported by NSF Grant No. ENG-76-15774 and NSF Grant No. ENG-78-06733.     

Almost periodic Jacobi matrices associated with Julia sets for polynomials

Let be the Jacobi matrix associated with polynomialT(z) of degreeN2. The spectrum of is the Julia set associated withT(z) which in many cases is a Cantor set. Let ⁽¹⁾ denote the result of omitting the first row and column ofJ. Then it is shown that the spectrum of ⁽¹⁾ may be purely discrete.It is also shown that forT(z)= ^NC_N(z/) for > , whereC _N is a Chebychev polynomial the coefficients of and ⁽¹⁾ are limit periodic extending the work of Bellissard, Bessis, and Moussa (Phys. Rev. Lett.49, 701–704 (1982)).Supported in part by N.S.F. grant DMS-8401609Supported in part by N.S.F. grant MCS-8203325     

Precise molecular weight distributions of high polymers by semiautomatic solvent extraction

It has been found practical to fractionate relatively monodisperse polystyrenes of molecular weights up to 4 × 10⁶ by using a semiautomatic solvent extraction procedure. The fractionators consist of flow-through mixing chambers provided with settling regions for the removal of finely suspended solid material. Provision is made for accurate control of both temperature and solvent–nonsolvent ratio. Two such apparatus, operated in tandem, were used in the present work; in principle, several more stages could be employed if desired for most polymer systems. Results on polystyrenes prepared in well defined ways appear to be in good agreement with predicted distributions. Applicability to other polymer systems is discussed.     

Tensor LEED analysis for the electrodeposited Pt(1 1 1)-(3×3)–Ag,I surface structure

A crystallographic analysis is reported using low-energy electron diffraction (LEED) in the tensor LEED approach for the electrodeposited coadsorption (3×3) structure with 4/9 monolayer (ML) of silver and 4/9 ML of iodine on the Pt(1 1 1) surface. The structure approximates a two-layer slice of bulk AgI cut parallel to its (1 1 1) plane and superimposed on the substrate with the Ag atoms in contact with the topmost Pt(1 1 1) layer, and the I atoms forming an overlayer on the Ag atoms. There are two types of Ag atoms in the (3×3) unit mesh; one type bonds to a single Pt atom, while the other type bonds to three Pt atoms. The average Ag–Pt bond distances are close to 2.48 and 2.82 Å respectively for the one and three-coordinate Ag atoms, but both types of Ag atoms bond to three I atoms with an average Ag–I distance of 2.67 Å. No significant corrugation is observed for either the I layer or the Ag layer.     

Interpretation of laser desorption mass spectra of unexpected inorganic species found in a cosmetic sample of forensic interest: fingernail polish

Monitoring of cell cultures in microbioreactors is a crucial task in cell bioassays and toxicological tests. In this work a novel tool based on a miniaturized sensor array fabricated using low-temperature cofired ceramics (LTCC) technology is presented. The developed device is applied to the monitoring of cell-culture media change, detection of the growth of various species, and in toxicological studies performed with the use of cells. Noninvasive monitoring performed with the LTCC microelectrode array can be applied for future cell-engineering purposes. Figure Microelectrode array for monitoring of cell cultures     

New chiral organosulfur donors related to bis(ethylenedithio)tetrathiafulvalene

Six new enantiopure chiral organosulfur donors, with structures related to BEDT-TTF, have been synthesised for use in the preparation of organic metals, starting either by double nucleophilic substitutions on the bis-mesylate of 2R,4R-pentane-2,4-diol or by a cycloaddition with subsequent elimination of acetic acid on the enol acetate of (+)-nopinone. Crystal structures of some of their radical cation triiodides salts and TCNQ complexes are reported.     

MOP-phosphonites: a novel ligand class for asymmetric catalysis

Chiral phosphonite ligands (S,R(b))-5a, (S,S(b))-5b, (R,R(b))-6a and (R,S(b))-6b are introduced, comprising a MOP-type backbone with a binol-based binaphthyl group bound to the phosphorus. Their reaction with [Pd(η(3)-C(4)H(7))Cl](2) affords η(3)-methallylpalladium chloride complexes 7a/b and 8a/b which have been isolated and structurally characterised. Solid-state and solution studies indicate subtle differences in their coordination behaviour, which ultimately affects their efficacy in the asymmetric hydrosilylation of styrene.     

Alkali metal complexes of sterically hindered mono- and di-carbanions containing Si-O bonds

The oxygen-bridged, silicon-substituted alkane {(Me3Si)2CH(SiMe2)}2O (1) may be prepared by the reaction of {(Me3Si)2CH}Li with ClSiMe2OSiMe2Cl in refluxing THF. Similarly, the alkane {(Me3Si)(Me2MeOSi)CH(SiMe2CH2)}2 (2) is readily accessible from the reaction between {(Me3Si)(Me2MeOSi)CH}Li and ClSiMe2CH2CH2SiMe2Cl under the same conditions. Compound 1 reacts with two equivalents of MeK to give the polymeric complex [[{(Me3Si)2C(SiMe2)}2O]K2(OEt2)]infinity [5(OEt2)] after recrystallisation. Treatment of 2 with two equivalents of either MeLi or MeK gives the corresponding complexes [{(Me3Si)(Me2MeOSi)C(SiMe2CH2)}2Li][Li(DME)3] [7(DME)3] and [{(Me3Si)(Me2MeOSi)C(SiMe2CH2)}2K2]n (8), respectively, after recrystallisation. Treatment of the alkane (Me3Si)2(Me2MeOSi)CH with one equivalent of MeK gives the polymeric complex [{(Me3Si)2(Me2MeOSi)C}K]infinity (3). These compounds have been identified by 1H and 13C{1H} NMR spectroscopy and elemental analyses and compounds 5(OEt2), 7(DME)3 and 3 have been further characterised by X-ray crystallography. Compound 7(DME)3 crystallises as a solvent-separated ion pair, whereas 5(OEt2) and 3 adopt polymeric structures in the solid state.